A Shock-Fitting Primer

Introduction

Prelude

The Curious Events Leading to the Theory of Shock Waves

Early Attempts at Computing Flows with Shocks

Shock-Fitting Principles

The Inviscid Burgers’ Equation

The One-Saw-Tooth Problem

Background Numerical Schemes

Mappings, Conservation Form, and Transformation Matrices

Boundary Shock-Fitting

Gaussian Pulse Problem

Boundary Shock-Fitting Revisited

Floating Shock-Fitting

Detection of Shock Formation

Application of Colombeau’s Generalized Functions to a Nonconservative System of Equations

Fundamental Concepts and Equations

Physical Problem

Mathematical Formulation

Explicit Form of the Equations of Motion

Orthogonal Curvilinear Coordinates

Differential Geometry of Singular Surfaces

Finite Discontinuities

Shock Wave Structure

Euler Equations: One-Dimensional Problems

Piston-Driven Flows

Numerical Analysis of a Simple Wave Region

Shock Wave Computation

Quasi-One-Dimensional Flows

Euler Equations: Two-Dimensional Problems

The Blunt Body Problem

External Conical Corners

Supersonic Flow over Elliptical Wings

Floating Shock-Fitting with Unstructured Grids

Introduction

Unstructured Grids: Preliminaries

Unstructured Grid Solver

Application to Euler Equations

Floating Shock-Fitting Implementation

Unstructured Grids Shock-Fitting Results

References

Appendix

Index